Issue 69

A. Almeida et alii, Frattura ed Integrità Strutturale, 69 (2024) 89-105; DOI: 10.3221/IGF-ESIS.69.07

currently studied in the field of structural mass optimization, for example, studies on minimizing the mass of structures subject to natural frequency constraints [3-7]. Although structural optimization is an effective tool, the combination of this with other tools is often necessary. Considering this context, the vibration control devices, classified as passive, active, and semi-active can be added to the structures to improve their performance against dynamic actions, and the optimization process can be also implemented to reach the maximum performance of these devices. The passive devices, which have pre-defined properties, are characterized by not using an external power source, while the active ones, which apply force to the structure at the same time as the excitation, need an external power source. The semi-active devices, which have been the object of several recent research, combine the advantages of passive and active devices simultaneously as they have an intrinsic characteristic of adaptability, being able to change their properties with a reduced amount of energy, without applying force to the structure. Among the semi-active control devices, the Magneto-Rheological (MR) dampers stand out, due to their mechanical simplicity, wide dynamic applicability, low energy cost, great strength, and robustness. These characteristics have shown good adherence to the demands of structural systems in the control of dynamic excitations such as earthquakes and wind [8]. Therefore, civil engineering can take advantage of this type of approach, creating structures able to monitor and control their response under dynamic excitations. Several studies have been published demonstrating the application of MR dampers in the control of dynamic responses. Among the first experimental studies with prototypes, there are those in which the authors developed experiments with structures of up to 6 degrees of freedom excited at the base in order to simulate an earthquake [9-11]. There are also numerical studies with simple structural models in which the authors developed simulations with structures of up to 20 degrees of freedom excited by earthquakes [12-15], and a study in which the authors developed simulations with a structure of 40 degrees of freedom excited by the wind [16]. It is also worth mentioning the more complex numerical models, such as the one in which the authors studied a structural model called mega-sub-controlled structure excited by wind [17] and the one in which the authors performed a simulation with a 2D frame excited by earthquakes [18]. Hybrid strategies using MR dampers and other types of devices are also being researched, for example in [19]. Finally, considering the theoretical experimental studies, there is a study in which the authors reported an experiment that was carried out on the cable-stayed Dongting Lake Bridge in China, severely excited by strong winds and rain [20], and the one in which the author analyzed several different structures, considering numerical models with multiple degrees of freedom excited by earthquakes [21]. As highlighted, most of these studies focus on analyzing simplified structural models subjected to earthquakes and, therefore, there is a lack of studies with more complex structural models, able to provide a better description of the behavior of tall buildings subjected to wind excitation. Additionally, unlike most works in the literature, this paper proposes a methodology in which not only the installation of dampers is considered as a way of minimizing vibration amplitudes, but also the optimization of the structure is carried out, with the objective of increasing the fundamental frequency of the building, taking it to values further away from the frequency content of the wind spectrum, and thus reducing the dynamic response. That is, the proposed methodology combines structural optimization with semi-active control devices. Besides, most of the works that propose different types of vibration control systems, for different types of structures and excitations, are related to passive systems, for example [22-42, among others]. Thus, to contribute to filling these gaps, this study focuses on analyzing a tall building, described by a 2D frame model of multiple degrees of freedom, under dynamic wind loading and controlled by semi-active MR dampers. For this, the dynamic responses of three different configurations of the building, under wind excitation, are analyzed, and compared with performance criteria indicated in [43] and [44]. The first configuration, called Original Uncontrolled (C1), consists of a frame building extracted from a tall building originally proposed and analyzed in [45]. The second, called Optimized Uncontrolled (C2), consists of a structure whose fundamental frequency was optimized, via the PSO algorithm, as a function of its mass, from the C1 configuration. The complete procedure for this optimization was presented by the authors in a previous paper [46]. The third and last one, called Optimized Controlled (C3), consists of the C2 configuration controlled through a set of semi-active MR dampers.

P ROBLEM FORMULATION AND PROPOSED METHODOLOGY

Structural modelling he numerical modelling of the structure is approached through the finite element method, considering a 2D frame model, according to the procedures from [47]. The damping matrix, C , was generated using the Rayleigh method, formulated as a linear combination of the global mass matrix, M , and global stiffness matrix, K . T

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